Patriots pick QB Jimmy Garoppolo in second round

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Eastern Illinois quarterback Jimmy Garoppolo (center) posed with NFL Commissioner Roger Goodell (right) and former Patriots linebacker Willie McGinest after being selected by New England in the second round.

Current backup Ryan Mallett has thrown four passes in three seasons and didn’t play a single snap in 2013. He was originally a third-round pick in 2011 and is entering the final year of his contract.

Before the NFL Draft began Thursday night, the Patriots and Texans were discussing a trade that would have sent Mallett to Houston, a league source confirmed to the Globe, but the trade never materialized.